Roadie — Your AI Tutor · Elliptic Curve Cryptography
Cryptography › Elliptic Curve Cryptography
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Roadie · AI Tutor

Let's explore Elliptic Curve Cryptography — the math behind CarKeys.

An elliptic curve is defined by the equation:

y² = x³ + ax + b

The key insight is that adding two points on a curve produces a third point, and this operation is easy to do but computationally impossible to reverse — that's what makes it secure.

Curve Equation math
# secp256k1 curve (used by Bitcoin & CarKeys) y² = x³ - 3x + 1 # Point operations Point addition: P + Q = R Scalar multiply: k × P = Public Key # Key relationship Private key k: secret integer Public key P: point on curve
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What makes ECC secure?
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So CarKeys uses this to generate keypairs?
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Roadie · AI Tutor

Exactly! CarKeys uses secp256k1 (the same curve as Bitcoin) for ECDSA signatures. Here's how it connects:

  • Your private key = random integer k
  • Your public key = k × G (generator point)
  • Signing = math using private key
  • Verification = math using public key only

Want to see how key rotation works next?

Next · Lesson 4 of 8
Key Rotation & Revocation
Learn how CarKeys handles keypair rotation — what triggers it, how the network reaches consensus on a new public key, and why revocation without a central authority requires cryptographic proofs.
Revocation lists Merkle proofs Threshold signatures Key ceremony